A 120 -ft flight control tower in the shape of a hyperboloid has hyperbolic cross sections perpendicular to the ground. Placing the origin at the bottom and center of the tower, the center of a hyperbolic cross section is 0 , 30 with one focus at 15 10 , 30 and one vertex at 15 , 30 . All units are in feet. a. Write an equation of a hyperbolic cross section through the origin. Assume that there are no restrictions on x or y . b. Determine the diameter of the tower at the base. Round to the nearest foot. c. Determine the diameter of the tower at the top. Round to the nearest foot.
A 120 -ft flight control tower in the shape of a hyperboloid has hyperbolic cross sections perpendicular to the ground. Placing the origin at the bottom and center of the tower, the center of a hyperbolic cross section is 0 , 30 with one focus at 15 10 , 30 and one vertex at 15 , 30 . All units are in feet. a. Write an equation of a hyperbolic cross section through the origin. Assume that there are no restrictions on x or y . b. Determine the diameter of the tower at the base. Round to the nearest foot. c. Determine the diameter of the tower at the top. Round to the nearest foot.
Solution Summary: The author calculates the equation of a hyperbolic cross section through the origin.
A
120
-ft
flight control tower in the shape of a hyperboloid has hyperbolic cross sections perpendicular to the ground. Placing the origin at the bottom and center of the tower, the center of a hyperbolic cross section is
0
,
30
with one focus at
15
10
,
30
and one vertex at
15
,
30
.
All units are in feet.
a. Write an equation of a hyperbolic cross section through the origin. Assume that there are no restrictions on
x
or
y
.
b. Determine the diameter of the tower at the base. Round to the nearest foot.
c. Determine the diameter of the tower at the top. Round to the nearest foot.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY